I've never slug hunted Deer, but have hunted Hogs with slugs. At 35-40 yards a Brenneke Black Magic will go all the way through a two foot thick Hog. It is a rifled slug and I shoot 2 3/4 short magnums. 1600 fps and one ounce slugs through a smooth bore. I've used both a modified choke barrel and a slug barrel.
The Brenneke sabot might be a better bet on Deer and good for some more distance.
Either the Black Magic or the Green Lighting in a 3 1/2 should go all the way through no problem.
Just opinion, but expansion in a slug is kind of redundant, a 12 gauge leaves a gaping 3/4 inch hole.
Brenneke also has rifled barrel slugs, I've never tried any.
Brenneke does slugs a little different, they seem a little hotter than most slugs, the slug doesn't discard the wad (or cup) and uses it to help stabilize the slug in regular smooth bore slug barrels. I'd guess they own the patent on the design and aren't sharing. There is no comparison to the old Remington slugs I used to shoot, the Brenneke just does slugs better than most.